Finite-History Outage Certification for Partially Observed Fluid Antenna Receivers

Abstract: Fluid antenna receivers can select a service position from partial port observations, but finite historical data leave uncertainty in the covariance used for that decision. We develop deployment-before-use reliability certification for a frozen partial-observation rule. A proper predictive density defines a history-based parameter region. Gaussian covariance envelopes, shared conditional-probability bounds and selector enclosures provide simultaneous risk bounds over continuous parameters and discontinuous port decisions. Separate history-coverage and integration budgets limit erroneous positive certification to 0.05 for a single qualification procedure under the stated stationary model and numerical assumptions. Confidence-set inclusion allows a new independent history to reuse the risk computation with the rule unchanged. In a structured Gaussian example with 32 candidate positions, five noisy probes and target outage 0.001, all 282 risk groups are qualified; the largest upper bound is 0.000999748. A separate coupled comparison gives a current-rule outage interval of $[7.6820,9.1266]\times10<sup>{-4}$ and resolves lower outage than two observed-port controls using the same historical fit. One independently recalibrated history reuses the certificate without additional risk sampling. Unresolved and adverse-member controls delimit this reuse.